Stable Model Predictive Control for Constrained Max-Plus-Linear Systems

Abstract

Discrete-event systems with synchronization but no concurrency can be described by models that are "linear" in the max-plus algebra, and they are called max-plus-linear (MPL) systems. Examples of MPL systems often arise in the context of manufacturing systems, telecommunication networks, railway networks, parallel computing, etc. In this paper we provide a solution to a finite-horizon model predictive control (MPC) problem for MPL systems where it is required that the closedloop input and state sequence satisfy a given set of linear inequality constraints. Although the controlled system is nonlinear, by employing results from max-plus theory, we give sufficient conditions such that the optimization problem that is performed at each step is a linear program and such that the MPC controller guarantees a priori stability and satisfaction of the constraints. We also show how one can use the results in this paper to compute a time-optimal controller for linearly constrained MPL systems.

Modeling and control of switching max-plus-linear systems with random and deterministic switching

“…This happens when x(k) represent the delay with respect to some constantly increasing reference signal (cf. Remark 8 and also see the shifted system (39) and (40) in Section 4 or in Necoara et al (2007)). …”

“…Just like we did in Necoara et al (2007) for max-plus-linear systems we can associate to every ρ a shifted system…”

Max-plus algebra and max-plus linear discrete event systems: An introduction

“…For more information on the analysis of max-plus linear time-invariant DES such as production systems, timetable dependent transportation networks, queuing systems, array processors, and so on the interested reader is referred to [1]- [3], [13], [14], [16], [17], [19], [32], [34], [40], [42]- [49] and the references therein.…”

Trajectory Tracking Control of a Timed Event Graph with Specifications Defined by a P-time Event Graph

“…As the complete analysis of these conditions needs an extensive study (see part 7.2 "Directions for future research" in [13]), we only give the following results.…”

“…Different authors give examples following this assumption on B (see [15], chapter 3 and 4 in [13] for instance).…”